Search results
Results from the WOW.Com Content Network
If we order the integers in the interval [1, 2n] by divisibility, the subinterval [n + 1, 2n] forms an antichain with cardinality n. A partition of this partial order into n chains is easy to achieve: for each odd integer m in [1,2 n ], form a chain of the numbers of the form m 2 i .
In computer science, an integer is a datum of integral data type, a data type that represents some range of mathematical integers. Integral data types may be of different sizes and may or may not be allowed to contain negative values. Integers are commonly represented in a computer as a group of binary digits (bits). The size of the grouping ...
In C++, associative containers are a group of class templates in the standard library of the C++ programming language that implement ordered associative arrays. [1] Being templates, they can be used to store arbitrary elements, such as integers or custom classes.
There are three important normal subgroups of prime power index, each being the smallest normal subgroup in a certain class: E p ( G ) is the intersection of all index p normal subgroups; G / E p ( G ) is an elementary abelian group , and is the largest elementary abelian p -group onto which G surjects.
Illustration of the Archimedean property. In abstract algebra and analysis, the Archimedean property, named after the ancient Greek mathematician Archimedes of Syracuse, is a property held by some algebraic structures, such as ordered or normed groups, and fields.
If all weights are integers, then the run-time can be improved to (+ ), but the resulting algorithm is only weakly-polynomial. [3] If the weights are integers, and all weights are at most C (where C >1 is some integer), then the problem can be solved in O ( m n log ( n ⋅ C ) ) {\displaystyle O(m{\sqrt {n}}\log(n\cdot C))} weakly ...
In other words, it is the number of integers k in the range 1 ≤ k ≤ n for which the greatest common divisor gcd(n, k) is equal to 1. [2] [3] The integers k of this form are sometimes referred to as totatives of n. For example, the totatives of n = 9 are the six numbers 1, 2, 4, 5, 7 and 8.
Another class of numbers Kaprekar described are Kaprekar numbers. [10] A Kaprekar number is a positive integer with the property that if it is squared, then its representation can be partitioned into two positive integer parts whose sum is equal to the original number (e.g. 45, since 45 2 =2025, and 20+25=45, also 9, 55, 99 etc.)